Simplify the following expression: $\sqrt{75}+\sqrt{27}+\sqrt{12}$
Explanation: First, try to factor any perfect squares out of the radicals. $= \sqrt{75}+\sqrt{27}+\sqrt{12}$ $= \sqrt{25 \cdot 3}+\sqrt{9 \cdot 3}+\sqrt{4 \cdot 3}$ Separate the radicals and simplify. $= \sqrt{25} \cdot \sqrt{3}+\sqrt{9} \cdot \sqrt{3}+\sqrt{4} \cdot \sqrt{3}$ $= 5\sqrt{3}+3\sqrt{3}+2\sqrt{3}$ Finally, simplify by combining the terms. $= ( 5 + 3 + 2 )\sqrt{3} = 10\sqrt{3}$